AGT duality [1]} relates 4-d \(\mathcal {N} = 2\)  quiver theories in a non-commutative \(\Omega \) -background à la Nekrasov-Shatasvili [2]}, [3]}, [4]} to 2-d Liouville CFT.
Denoting by \({\epsilon _1},{\epsilon _2}\)  the quantum deformation parameters and by
\(b = \sqrt{\frac{\epsilon _1}{\epsilon _2}}\) , the central charge of the CFT is given by
\(c = 1 + 6 Q^2\quad {\rm with} \quad Q = b + \frac{1}{b}\) 
